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Mean-Field Analysis Of The Layering Transitions Of The Spin- 1/2 Ising Model In A Transverse Magnetic Field.

Moses Eterigho Emetere

Published May 23, 2011• 1 citation
OpenAlex

Abstract

The effect of the transverse and longitudinal magnetic field on the layering transition of the spin-1/2 Ising model was investigated using the mean field theory. The spin variables used for layering phase transition reveals its nature as ‘glassy’. It was shown that (under the spin-1/2 Ising model) there were no significant result when N>2 in the presence of transverse magnetic field.

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The effect of the transverse and longitudinal magnetic field on the layering transition of the spin-1/2 Ising model was investigated using the mean field theory. The spin variables used for layering phase transition reveals its nature as ‘glassy’. It was shown that (under the spin-1/2 Ising model) there were no significant result when N>2 in the presence of transverse magnetic field.
We have studied the phase transition behaviour of the random field Ising model in the presence of a transverse (or tunnelling) field. The mean field phase diagram has been studied in detail, and in particular the nature of the transition induced by the tunnelling (transverse) field at zero temperature. A modified hyperscaling relation for the zero-temperature transition has been derived using the Suzuki - Trotter formalism and a modified `Harris criterion'. A mapping of the model to a randomly diluted antiferromagnetic Ising model in uniform longitudinal and transverse field is also given.
The effect of a random transverse field (RTF) on the wetting and layering transitions of a spin-1/2 Ising model, in the presence of bulk and surface fields, is studied within an effective field theory by using the differential operator technique. Indeed, the dependencies of the wetting temperature and wetting transverse field on the probability of the presence of a transverse field are established. For specific values of the surface field we show the existence of a critical probability pc above which wetting and layering transitions disappear.
The effect of a random transverse field (RTF) on the wetting and layering transitions of a spin-1/2 Ising model, in the presence of bulk and surface fields, is studied within an effective field theory by using the differential operator technique. Indeed, the dependencies of the wetting temperature and wetting transverse field on the probability of the presence of a transverse field are established. For specific values of the surface field we show the existence of a critical probability pcp_{c}pc​ above which wetting and layering transitions disappear.
The effect of edge on wetting and layering transitions of a three-dimensional spin-1/2 Ising model is investigated, in the presence of longitudinal and surface magnetic fields, using mean field theory and Monte Carlo simulations. For T=0, the ground state phase diagram shows that there exist only three allowed transitions, namely, surface and bulk transition, surface transition, and bulk transition. However, there exist a surface intralayering temperature T(s)(L), above which the surface and the intralayering surface transitions occur. While the bulk layering and intralayering transitions appear above another finite temperature T(b)(L)(>or=T(s)(L)). These surface and bulk intralayering transitions are not seen in the perfect surfaces case. Numerical values of T(s)(L) and T(b)(L), computed by Monte Carlo method are found to be smaller than those obtained using mean field theory. However, the results predicted by the two methods become similar, and are exactly those given by the ground state phase diagram, for very low temperatures. On the other hand, the behavior of the local magnetizations as a function of the external magnetic field, shows that the transitions are of the first order type. T(s)(L) and T(b)(L) decrease when increasing the system size and/or the surface magnetic field. In particular, T(b)(L) reaches the wetting temperature T(w) for sufficiently large system sizes.